Question

There are 980 students in a school, of which 50% play cricket, 30% play basketball and 40% play football. If 60 students play cricket and basketball, 48 students play basketball and football, 180 students play cricket and football, and 35 students play all the three games, then how many students play none of the games?

• A. 73
• B. 67
• C. 63
• D. 57

Hint:

Apply the principle of inclusion and exclusion when three overlapping sets are involved.

Answer 1

The Correct Option is D

Let \( n(C) = 490 \), \( n(B) = 294 \), \( n(F) = 392 \), \( n(C \cap B) = 60 \), \( n(B \cap F) = 48 \), \( n(C \cap F) = 180 \), \( n(C \cap B \cap F) = 35 \) Using inclusion-exclusion: \[ n(C \cup B \cup F) = 490 + 294 + 392 - 60 - 48 - 180 + 35 = 923
\Rightarrow \text{None} = 980 - 923 = 57 \] Correct value: 57